A simple model for interannual sand bar behavior

Abstract

Time and length scales of beach variability have been quantified using 16 years of beach surveys sampled at the Army Corps of Engineers' Field Research Facility, located on the U.S. Atlantic coast. Between 50% and 90% of the bathymetric variability at this site was explained by alongshore-uniform response over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or higher than 1 cycle/yr, more than 80% of the bathymetric variance at all cross-shore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the low-frequency variability. The observed behavior can be explained by a simple, heuristic model. The model assumes that bars migrate toward a wave height dependent equilibrium position. This position was shown to coincide with the wave “breakpoint.” Additionally, the rate of bar response is taken to be variable and was empirically determined to be proportional to the wave height cubed. The net effect of a variable response rate is to shift the expected long-term mean sandbar position offshore, toward the equilibrium position associated with the largest waves. The model explained up to 80% of the observed bar position time series variance and up to 70% of the variance of bar crest velocity time series, which were extracted from three different sandbars. Characteristic bar response times (related to the inverse of the response rate) were found to be long relative to the characteristic timescale of the forcing (1 year in our case). As a result, transient response (i.e., bar position far from equilibrium) tended to persist for many cycles of the forcing. Transient bar behavior appears in the observations when bars formed near the shoreline or when outer bars decayed and inner bars faced a changed wave climate. While the present model is able to explain the evolution of these transients, it does not contain a mechanism for their introduction.

abstract = "Time and length scales of beach variability have been quantified using 16 years of beach surveys sampled at the Army Corps of Engineers' Field Research Facility, located on the U.S. Atlantic coast. Between 50{\%} and 90{\%} of the bathymetric variability at this site was explained by alongshore-uniform response over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or higher than 1 cycle/yr, more than 80{\%} of the bathymetric variance at all cross-shore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the low-frequency variability. The observed behavior can be explained by a simple, heuristic model. The model assumes that bars migrate toward a wave height dependent equilibrium position. This position was shown to coincide with the wave “breakpoint.” Additionally, the rate of bar response is taken to be variable and was empirically determined to be proportional to the wave height cubed. The net effect of a variable response rate is to shift the expected long-term mean sandbar position offshore, toward the equilibrium position associated with the largest waves. The model explained up to 80{\%} of the observed bar position time series variance and up to 70{\%} of the variance of bar crest velocity time series, which were extracted from three different sandbars. Characteristic bar response times (related to the inverse of the response rate) were found to be long relative to the characteristic timescale of the forcing (1 year in our case). As a result, transient response (i.e., bar position far from equilibrium) tended to persist for many cycles of the forcing. Transient bar behavior appears in the observations when bars formed near the shoreline or when outer bars decayed and inner bars faced a changed wave climate. While the present model is able to explain the evolution of these transients, it does not contain a mechanism for their introduction.",

N2 - Time and length scales of beach variability have been quantified using 16 years of beach surveys sampled at the Army Corps of Engineers' Field Research Facility, located on the U.S. Atlantic coast. Between 50% and 90% of the bathymetric variability at this site was explained by alongshore-uniform response over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or higher than 1 cycle/yr, more than 80% of the bathymetric variance at all cross-shore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the low-frequency variability. The observed behavior can be explained by a simple, heuristic model. The model assumes that bars migrate toward a wave height dependent equilibrium position. This position was shown to coincide with the wave “breakpoint.” Additionally, the rate of bar response is taken to be variable and was empirically determined to be proportional to the wave height cubed. The net effect of a variable response rate is to shift the expected long-term mean sandbar position offshore, toward the equilibrium position associated with the largest waves. The model explained up to 80% of the observed bar position time series variance and up to 70% of the variance of bar crest velocity time series, which were extracted from three different sandbars. Characteristic bar response times (related to the inverse of the response rate) were found to be long relative to the characteristic timescale of the forcing (1 year in our case). As a result, transient response (i.e., bar position far from equilibrium) tended to persist for many cycles of the forcing. Transient bar behavior appears in the observations when bars formed near the shoreline or when outer bars decayed and inner bars faced a changed wave climate. While the present model is able to explain the evolution of these transients, it does not contain a mechanism for their introduction.

AB - Time and length scales of beach variability have been quantified using 16 years of beach surveys sampled at the Army Corps of Engineers' Field Research Facility, located on the U.S. Atlantic coast. Between 50% and 90% of the bathymetric variability at this site was explained by alongshore-uniform response over the approximately 1 km alongshore span of the surveys. Although the incident wave height variance was dominated by frequencies at or higher than 1 cycle/yr, more than 80% of the bathymetric variance at all cross-shore locations was explained by frequencies <1 cycle/yr. Interannual cycles consisting of sandbar formation, migration, and decay contributed to the low-frequency variability. The observed behavior can be explained by a simple, heuristic model. The model assumes that bars migrate toward a wave height dependent equilibrium position. This position was shown to coincide with the wave “breakpoint.” Additionally, the rate of bar response is taken to be variable and was empirically determined to be proportional to the wave height cubed. The net effect of a variable response rate is to shift the expected long-term mean sandbar position offshore, toward the equilibrium position associated with the largest waves. The model explained up to 80% of the observed bar position time series variance and up to 70% of the variance of bar crest velocity time series, which were extracted from three different sandbars. Characteristic bar response times (related to the inverse of the response rate) were found to be long relative to the characteristic timescale of the forcing (1 year in our case). As a result, transient response (i.e., bar position far from equilibrium) tended to persist for many cycles of the forcing. Transient bar behavior appears in the observations when bars formed near the shoreline or when outer bars decayed and inner bars faced a changed wave climate. While the present model is able to explain the evolution of these transients, it does not contain a mechanism for their introduction.